What we didn't like has already been explained to you. Please either take a basic physics course, or read a good basic text book on physics, not just "popular" books or web sites. You are using words, whose definitions you don't understand, in ways that do not make sense. As for your last post, "energy" is NOT "matter". That is NOT what "e= mc^2" means!

The most common example is three dimensional space (3-space). It takes 3 numbers to locate a point in 3-space. Another example is a 4-vector which takes 4 numbers to define it. Spacetime is an another example of a mathematical object which requires 4 numbers to define a point in spacetime. Such a point is called an event.

The 4-vector known as 4-momentum. P is properly defined as

P = (mc, p)

where

m = relativistic massp = 3-momentum.

m is the time component of 4-momentum.

What is the object of which you assert that E is a component of?

I can't address the rest of your post until you are able to clearly state or defined the object is that you claim that energy is a component of.

Hi PittsburghJoe,
I'm not sure that I understand your post,
however you might like to consider the <Four Dimensional Momentum> vector.
Note how mass appears in the space-wise components and Energy in the time-wise component.

In general the energy of an object is the time component of the 4-form associated with the 4-momentum of the object, not the time component of the 4-momentum. I.e. in general

E = P_0, not P^0

There's a sign that I'm leaving out since it depends on the signature of the metric.

In physics the term "dimension" is generally reserved for the four components of the vectors defining relative positions in spacetime.

I'm a bit confused as to what you mean by "generally." Can you explain, please?

The reason I ask is because depending on which dictionary one uses the term generally is defined in two ways. Its why I hate it when I use the term. Lol!!

E.g. do a search on "generally definition" using Google and these definitions will pop up

1. in most cases; usually.

2. in general terms; without regard to particulars or exceptions.

Confusing, isn't it?

So do you mean that in all cases In physics the term "dimension" is reserved for the four components of the vectors defining relative positions in spacetime. or in most cases?

If its all cases then I disagree. E.g. spinors are used in quantum mechanics and spinor, the components of which are not components of spacetime. In fact the spinor which represents spin only has two components, i.e. a spinor is a two-element column vector.

My point being that there are other objects in physics which have dimensions, not just in string theory (which I'm ignorant of).

What we didn't like has already been explained to you. Please either take a basic physics course, or read a good basic text book on physics, not just "popular" books or web sites. You are using words, whose definitions you don't understand, in ways that do not make sense. As for your last post, "energy" is NOT "matter". That is NOT what "e= mc^2" means!

Many members don't know math and wouldn't be able to follow along in a course at the level I think you have in mind. He'd be better off learning math first, after which he wouldn't need to learn the physics you're referring to because he'd learn that he's using the term "dimension" incorrectly.

pittsburghjoe - Please take notice of the fact that while spacetime and a 4-vector are both 4-dimensional objects. Spacetime is what is known as a manifold, which is a fancy name for a set of points with certain properties. I'd also like to note that nothing that you said is correct.

There is another use of the term "dimension" in physics ii as it pertains to physical dimensions, i.e. to refer to the units in which something is measured. For example: the IS dimensions of area is the square meters, force is the Newton, charge the Coulomb. See:https://en.wikipedia.org/wiki/Dimensional_analysis

In any branch of science there are well-defined terms, mass, energy and time being some of them. It serves no useful purpose to anybody to define them differently. Only confusion can result from that. It can be useful to discuss whether a term should be defined in a given way. Those conversations even appear in the American Journal of Physics. But that's different than what you're doing here. And I can promise you that nothing you posted here would be good in any physics textbook so no, it's not time to rewrite any textbook. I don't wish to be rude, that's not my intent. I'm merely trying to help you understand what you're doing wrong.

This is a physics help forum. Its not a New Theories forum. The purpose of this forum is to help people learn and understand mainstream physics.

To the rest - It just occurred to me that there is a sense in which one can say that energy is a dimension just like time and that's as I spoke of it above, i.e. energy is a dimension of a 4form, namely the energy-momentum 4-form just like time is said to be dimension of spacetime. Although that's a sloppy use of the term dimension its in common use. Sigh!! Lol!